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Asymptotic properties of the Radon transform in \({\mathbb{R}}^ n\). (English) Zbl 0627.44005

Following a suggestion of A. L. Yakymiv [Mat. Sb., Nov. Ser. 115(157), 463-477 (1981; Zbl 0469.60085)] classes \(RV_{\alpha}({\mathbb{R}}^ n)\), \(RV_{\alpha}(S^{n-1}\times {\mathbb{R}}^ 1)\) of regularly varying functions of index \(\alpha\) on \({\mathbb{R}}^ n\), \(S^{n-1}\times {\mathbb{R}}^ 1\) are introduced. The Radon transform of f is denoted by \(\hat f.\) Theorem 3.1: If \(\alpha <n-1\), then \(\hat f\in RV_{\alpha +n-1}(S^{n-1}\times {\mathbb{R}}^ 1)\). A similar theorem is given for f restricted to a cone.
Reviewer: F.Natterer

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
47B38 Linear operators on function spaces (general)

Citations:

Zbl 0469.60085
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